CSC 270 - Survey of Programming Languages: Scheme (Racket)

Conditional Expressions and Programs

Booleans and Relations

• Computer programs have to be able to handle different sets of data in different ways.
  • A game has to determine if a player is within a certain part of the screen.
  • Employees for XYZ & Co.may work between 12 and 65 hours. Any number outside this range is not valid.

Conditions

• Conditions are mathematical statements that are either true or false.

E.g., a number is either equal, less than or greater than another number.
x = y		x is equal to y
x > y		x is greater than y
x < y		x is less than y

• These statements are either true or false.
• If x = 4 and y=5. which of these statements are true? Which are false?

Compound Conditions

• Sometimes a statement may be composed of several simpler statements and its truth depends on the truth of these simpler statements.
• E.g.

  x = y AND x < y AND x > y
  x = y OR x < y OR x > y
  x = y AND x > y

• Which of these are true? Which are false?

Conditions in Scheme

• In Scheme, the "words" for "true" and "false" are true and false respectively.
• Conditional expressions are written with the relational operator (which tells us whether they're equal, not equal, less than, etc.) before the two values being compared.

  (= x y)	x is equal to y
  (> x y)	x is greater than y
  (< x y) 	x is less than y

• What happens when you enter

  (< 4 5)
  (= 4 5)

• Compound conditions are written by placing the logical operator (and, or, & not) before the simple logical expression(s).

  (and (= x y) (< y z))
  (or (= x y) (< y z))
  (not (= x y))
  (and (= 5 5) (< 5 6))
  (and (= 5 5) (< 5 5))

Programs That Test Conditions

• The following program tests whether a number is 5

  ;; is 5 : number --> boolean
  ;; to determine whether n is equal to 5
  (define (is5 n)
  	( = n 5)) 

• The following program tests whether a number is between 5 & 6:

  ;; is-between-5-6 : number --> boolean
  ;; to determine whether n is between 5 and 6 ;;(exclusive)
  (define (is-between-5-6 n)
  	(and ( < 5 n) (< n 6))) 

• The following program tests whether a number is between 5 & 6 or over 10:

  ;; is-between-5-6-or-over-10 : number --> boolean
  ;; to determine whether n is between 5 and 6 ;;(exclusive) or greather than or equal to 10
  (define (is-between-5-6-or-over-10 n)
  	(or (and ( < 5 n) (< n 6))
  	(>= n 10))) 

Conditional Programs

• Conditions are most useful in the context of a program.
  • We call the programs that use them conditional programs.
  • We formulate them using conditional expressions.
• The general forms of a conditional expression is:

  (cond					(cond
     [question answer]			   [question answer]
       ....                     or                  ...
     [question answer])			   [else answer])

Designing Conditional Programs

• Example -a bank pays higher interestrates to depositors with larger balances:

  over $10,000				6%
  over $5000 and up to $10,000		5.5%
  over $1000 and up to $5000			4.5%
  up to $1000				4% 

• How do we write this in Scheme?

  (cond 
  	[(<= n 1000) .040]
  	[(<= n 5000) .045]
  	[(<= n 10000) .055]
  	[( > n 10000) .060])

• This expression allows us to consider bad data, where we return an interest rate of 0.0

  (cond 
  	[(<= n 1000) .040]
  	[(<= n 5000) .045]
  	[(<= n 10000) .055]
  	[( > n 10000) .060]
  	[else 0.0])

• How do we use this in a program

  (define (interest-rate amount)
  (cond 
  	[(<= amount 1000) .040]
  	[(<= amount 5000) .045]
  	[(<= amount 10000) .055]
  	[( > amount 10000) .060]
  	[else 0.0]))

Designing Conditional Programs

• Developing conditional programs are more complicated. It requires that the problem statement list the different cases.
• The necessary steps in developing conditional programs:
  • Data Analysis - Identifying all the various data situations
  • Program Examples - to illustrate the different situations
  • The Program Body
    • Conditions - expressing the situation as conditional expressions
    • Answers - what happens in this case.
  • Simplification - is there a simpler way to state the same thing that is correct?

Data Analysis

• Let's draw a number line to identify the different intervals that correspond to a specific situation.

  ;; interest-rate : number --> number
  ;; to determine the interest rate for the given amount >= 0
  (define (interest-rate amount) ...)

Program Examples

• Our interest rates are in the 0-1000, 1000-5000 and 5000+ ranges.
• We pick numbers in each range so that we can run test cases.
• We'll pick 500, 2000 and 7000 as examples.

Program Body - Conditions

• The general framework is:

  (define (interest-rate amount)
  	(cond
  		[....]
  		[....]
  		[....]))

• The conditions are:

  (and (<= 0 amount) (<= amount 1000))
  (and (< 1000 amount) (<= amount 5000))
  (> amount 5000)

• Our program becomes:

  (define (interest-rate amount)
  	(cond
  		[(and (<= 0 amount) (<= amount 1000))...]
  		[(and (< 1000 amount) (<= amount 5000))...]
  		[(> amount 5000)...]))

Program Body - Answers

• Values
  • The answer for the 0-1000 case is 4.0
  • The answer for the 1000-5000 case is 4.5
  • The answer for the 5000+ case is 5.0
• The program becomes:

  (define (interest-rate amount)
  	(cond
  		[(and (<= 0 amount) (<= amount 1000)) 4.0]
  		[(and (< 1000 amount) (<= amount 5000))4.5]
  		[(> amount 5000)5.0]))

Simplication

• When the definition is completed and tested, a programmer may wish to simplify it.
• In our case, we can rewrite this:

  (define (interest-rate amount)
  	(cond
  		[(<= amount 1000) 4.0]
  		[(<= amount 5000)4.5]
  		[else 5.0]))

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